How do I add physics to cartoon styled hair?
You have to create a flat hair mesh and apply the physics on it. Then you need to add a Surface Deform Modifier on your hair model to take the transformation information from the flat hair mesh. This method works especially well on long hair. The setup would look like this:


When working with Surface Deform keep in mind to cover your  entire hair model with that flat hair mesh. And also do me a favor and make a better flat hair mesh that I did here. It was just a really quick prove of concept.